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Spaces of Holomorphic Functions in the Unit Ball

  • Kehe┬áZhu

Part of the Graduate Texts in Mathematics book series (GTM, volume 226)

Table of contents

  1. Front Matter
    Pages I-X
  2. Pages 1-38
  3. Pages 39-78
  4. Pages 79-108
  5. Pages 109-156
  6. Pages 199-234
  7. Pages 235-262
  8. Back Matter
    Pages 263-271

About this book

Introduction

There has been a flurry of activity in recent years in the loosely defined area of holomorphic spaces. This book discusses the most well-known and widely used spaces of holomorphic functions in the unit ball of C^n. Spaces discussed include the Bergman spaces, the Hardy spaces, the Bloch space, BMOA, the Dirichlet space, the Besov spaces, and the Lipschitz spaces. Most proofs in the book are new and simpler than the existing ones in the literature. The central idea in almost all these proofs is based on integral representations of holomorphic functions and elementary properties of the Bergman kernel, the Bergman metric, and the automorphism group.

The unit ball was chosen as the setting since most results can be achieved there using straightforward formulas without much fuss. The book can be read comfortably by anyone familiar with single variable complex analysis; no prerequisite on several complex variables is required. The author has included exercises at the end of each chapter that vary greatly in the level of difficulty.

Kehe Zhu is Professor of Mathematics at State University of New York at Albany. His previous books include Operator Theory in Function Spaces (Marcel Dekker 1990), Theory of Bergman Spaces, with H. Hedenmalm and B. Korenblum (Springer 2000), and An Introduction to Operator Algebras (CRC Press 1993).

Keywords

Complex analysis bounded mean oscillation holomorphic function integral

Authors and affiliations

  • Kehe┬áZhu
    • 1
  1. 1.Department of MathematicsState University of New York at AlbanyAlbanyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/0-387-27539-8
  • Copyright Information Springer Science+Business Media, Inc. 2005
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-22036-9
  • Online ISBN 978-0-387-27539-0
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site